The 2nd ISSP-MPIPKS Joint Workshop

Dynamics of Strongly Correlated Systems March 30–31, 2015

Main Lecture Hall of the Institute for Solid State Physics, The University of Tokyo Mar$30$(Mon)$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $

10:00$–$ 10:05$ Opening$address$ $ $ (Masashi$Takigawa,$Director$of$ISSP)$

10:05$–$ 10:15$ ISSP$and$MPIBPKS$ $ $ (Kazuo$Ueda,$Former$director$of$ISSP)$

! Topological!state,!entanglement,!and!correlation!

10:15$–$ 10:55$ Frank$Pollmann*$ $ $ (MaxBPlanckBInstitut$für$Physik$komplexer$Systeme)$

$ $ Entanglement,$and$dynamics$in$manyBbody$localized$systems$

10:55$–$ 11:35$ Masaki$Oshikawa*$ $ $ (The$Institute$for$Solid$State$Physics)$

$ $ Symmetry$protection$of$critical$phases$and$global$anomaly$in$1+1$dimensions$

11:35$–$ 12:15$ Toshikaze$Kariyado$ $ $ (University$of$Tsukuba)$

$ $Correlation$effects$on$the$topological$edge$states$in$graphene$nanoflakes:$ $Relation$between$nanostructure$and$local$magnetic$order

12:15$–$ 13:30$ lunch$

! Nonequilibrium!Mott!physics!and!charge!properties!

13:30$–$ 14:10$ Ichiro$Terasaki*$ $ $ (Nagoya$University)$ $ $

$ $ The$Mott$insulator$Ca2RuO4$in$a$nonBequilibrium$steady$state 14:10$–$ 14:50$ Akira$Ueda*$ $ $ (The$Institute$for$Solid$State$Physics)$

$ $HydrogenBbonded$ purely$ organic$ conductors:$ Exploration$ of$ hydrogenBbondB$dynamicsBcoupled$electronic$properties$

14:50$–$ 15:05$ break$

! Dynamics!in!frustrated!systems!

15:05$–$ 15:45$ Mathieu$Taillefumier*$ $ $ (Okinawa$Institute$of$Science$and$Technology)$

$ $SemiBclassical$ spin$ dynamics$ of$ the$ antiferromagnetic$ Heisenberg$ model$ on$ the$kagome$lattice$

15:45$–$ 16:25$ Masafumi$Udagawa*$ $ $ (The$University$of$Tokyo)$

$ $Emergent$collective$excitations$and$anomalous$dynamics$of$spin$ice$with$shortBrange$interaction$

16:25$–$ 17:50$ poster$session$

18:00$–$ 20:00$ banquet$

Mar$31$(Tue)$

! QCP!and!topological!phases!

9:00$–$ 9:40$ Yosuke$Matsumoto*$ $ $ (The$Institute$for$Solid$State$Physics)$

$ $ Emergent$critical$phase$in$a$correlated$electron$system$

9:40$–$ 10:20$ Tsuneya$Yoshida$ $ $ (RIKEN)$

$ $ Classification$ of$ twoBdimensional$ symmetry$ protected$ topological$ phases$ with$ a$reflection$symmetry$

10:20$–$ 10:35$ break$

! Quantum!spin!ice!

10:35$–$ 11:15$ Kenta$Kimura*$ $ $ (Osaka$University)$

$ $ Quantum$fluctuations$in$exchangeBbased$spin$ice$Pr2Zr2O7

11:15$–$ 11:55$ Olga$Petrova*$ $ $ (MaxBPlanckBInstitut$für$Physik$komplexer$Systeme)$

$ $ Magnetic$monopoles$in$diluted$quantum$spin$ice$

11:55$–$ 13:20$ lunch$

! Skyrmion!and!Higgs!mode!

13:20$–$ 14:00$ Naoto$Nagaosa*$ $ $ (RIKEN$and$The$University$of$Tokyo)$

$ $ Dynamics$of$coupled$electrons,$skrymions$and$monopoles$

14:00$–$ 14:40$ Naoto$Tsuji$ $ $ (The$University$of$Tokyo)$

$ $ LightBinduced$HiggsBmode$resonance$in$sBwave$and$dBwave$superconductors$

14:40$–$ 14:55$ break$

! Quantum!spin!liquids!

14:55$–$ 15:35$ Yoshitomo$Kamiya*$ $ $ (RIKEN)$

$ $ Solidifying$a$quantum$spin$liquid$in$a$3D$toric$code$

15:35$–$ 16:15$ Dima$Kovrizhin*$ $ $ (University$of$Cambridge)$

$ $ Dynamics$in$quantum$spinBliquids$

16:15$–$ 16:20$ Closing$address$ $ $ (Hirokazu$Tsunetsugu,$ISSP)$

$ $ (*:$invited$speakers)$

$ Poster$session$

PSB01$ Koudai$Iwahori$ $ $ (Kyoto$University)$$ PeriodicallyBdriven$Kondo$impurity$coupled$to$an$ultracold$fermionic$bath$

PSB02$ Masaya$Nakagawa$ $ $ (Kyoto$University)$

$ PhotoBinduced$Kondo$effect$and$its$anomalous$behavior$

PSB03$ Akihisa$Koga$ $ $ (Tokyo$Institute$of$Technology)$$ Transport$properties$for$a$quantum$dot$coupled$to$normal$leads$with$the$pseudogap$structure$

PSB04$ Yuta$Murakami$$ $ $ (The$University$of$Tokyo)$

$ Dynamical$meanBfield$analysis$of$nonBequilibrium$relaxation$processes$ $in$an$electronBphonon$coupled$system$

PSB05$ Takumi$Ohta$ $ $ (Yukawa$Institute$for$Theoretical$Physics)$

$ Phase$diagram$of$a$oneBdimensional$generalized$cluster$model$and$dynamics$ $during$an$interaction$sweep$

PSB06$ Yuya$Nakagawa$ $ $ (The$Institute$for$Solid$State$Physics)$$ Flux$quench$in$the$S=1/2$XXZ$chain$

PSB07$ Kazuaki$Takasan$ $ $ (Kyoto$University)$$ Topological$Kondo$insulators$in$strong$laser$fields$

PSB08$ Satoru$Maeda$ $ $ (Kyushu$Institute$of$Technology)$$ Effect$of$CaBdoping$on$pyrochlore$iridates$Nd2Ir2O7$

PSB09$ Kim$HyeonBDeuk$ $ $ (Kyoto$University)$

$ Dynamical$analyses$of$condensedBphase$hydrogens$using$nuclear$ $and$electron$wave$packet$molecular$dynamics$simulation$

PSB10$ Tomoyuki$Hamada$ $ $ (Hitachi$Ltd.)$

$ First$principle$calculation$of$electronic$structures$of$lantanide$oxides$ $with$pseudopotential$method$

PSB11$ Takeru$Nakayama$ $ $ (The$Institute$for$Solid$State$Physics)$$ Fano$resonance$between$Higgs$bound$states$and$NambuBGoldstone$modes$

PSB12$ Katsuaki$Kobayashi$ $ $ (University$of$ElectroBCommunications)$$ Convergence$for$the$groundstate$auxiliary$field$method$

PSB13$ Amane$Uehara$ $ $ (The$University$of$Tokyo)$

$ Theoretical$study$of$chargeBspinBorbital$fluctuations$in$mixed$valence$spinels:$ $AlV2O4$and$LiV2O4$

PSB14$ Yusuke$Sugita$ $ $ (The$University$of$Tokyo)$$ Excitonic$multipole$order$in$a$dBp$model$with$parity$mixing$

PSB15$ Joji$Nasu$ $ $ (Tokyo$Institute$of$Technology)$$ Finite$temperature$phase$transition$in$chiral$spin$liquids$

PSB16$ Takanori$Sugimoto$ $ $ (Tokyo$University$of$Science)$$ Magnetization$process$in$a$frustrated$spin$ladder$

PSB17$ Kazuhiko$Tanimoto$ $ $ (Yukawa$Institute$for$Theoretical$Physics)$$ Topological$quantum$phase$transition$in$an$SU(N)Binvariant$spin$chain$

PSB18$ Ryo$Ozawa$ $ $ (The$University$of$Tokyo)$$ Meron$crystals$with$spin$scalar$chiral$stripes$

PSB19$ Hiroyuki$Fujita$ $ $ (The$Institute$for$Solid$State$Physics)$$ Chiral$magnetic$effect$in$insulators$

Oral� �Presentations�

Entanglement and dynamics in Many-Body Localized Systems

R. Singh1, J. Kjall2, J. H. Bardarson 1, F. Pollmann1

1Max Planck Institute for the Physics of Complex Systems Noethnitzer Str. 38 D-01187 Dresden

Germany

2Department of Physics, Stockholm University Albanova University Center SE-106 91 Stockholm

Sweden

Many-body localized (MBL) phases occur in isolated quantum systems when Anderson lo-calization persists in the presence of finite interactions. It turns out that the entanglement is avery useful quantity to study these phases. First, we use the bipartite entanglement of excitedeigenstates to pinpoint a phase transition from a localized to an extended phase in a randomIsing chain with short ranged interactions [1]. A characterizing property of the MBL phase isthat the area law also applies to excited states. Thus, in one-dimensional systems, these statescan be encoded e�ciently using a matrix-product state representation. Second, we study thetime evolution of simple (unentangled) initial states for a system of interacting spinless fermionsin a one dimensional system. It is found that interactions induce a dramatic change in thepropagation of entanglement.

References[1]J. A. Kjall, J. H. Bardarson, and F. Pollmann, Phys. Rev. Lett. 113, 107204 (2014).

Symmetry protection of critical phases and

global anomaly in 1 + 1 dimensions

Shunsuke C. Furuya1 and Masaki Oshikawa21Department of Quantum Matter Physics, University of Geneva, 24 Quai Ernest-Ansermet 1211

Geneva, Switzerland

2Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan

Classification of quantum phases is a central problem in condensed matter and statisticalphysics. They can be first classified into gapped and gapless phases. Gapped quantum phasesare relatively easier to be handled theoretically. In fact, there has been a significant progressin further classification of gapped phases. In particular, symmetry protected topological (SPT)phases has become an important concept in the classification [1]. That is, even when two stateshave no long-range entanglement and are indistinguishable in terms of any local observables, inthe presence of a certain symmetry, they could still belong to distinct phases separated by aquantum phase transition.

In contrast, classification of gapless quantum phases remains very much open. Symmetriesare naturally expected to play an important role also in the classification of gapless quantumphases. Interestingly, symmetry protection of gapless quantum phases has been better under-stood for the gapless edge states of SPT phases. As a simple and well-known example, the helicaledge state of a topological insulator remains gapless even in the presence of impurities, as longas the system is time-reversal invariant. This indeed leads to the stability of the topologicalinsulator as an SPT phase in the presence of the time-reversal symmetry. This approach is re-cently refined and generalized in terms of anomaly [2]. In short, the edge state of an SPT phaseexhibits an anomaly with respect to the relevant symmetry, which implies the “ingappability”of the edge state in presence of the symmetry. This also motivates us to question if there is amechanism of symmetry protection of the universality class of bulk gapless critical phases.

In this talk, we argue that there is a protection of bulk gapless critical phases by discretesymmetry. This symmetry protection is quite analogous to that of the well-known (gapped) SPTphases; here we show that the concept can be generalized to bulk gapless critical phases. Wedemonstrate this for the SU(2)-symmetric quantum antiferromagnetic chains and their e↵ectivefield theory, SU(2) Wess-Zumino-Witten (WZW) theory as an example. The SU(2) WZW theoryis characterized by a natural number k, which is called level. Hereafter we denote the level-kSU(2) WZW theory as SU(2)k WZW theory. The SU(2)k WZW theories with k = 1, 2, . . .are thought to be a complete classification of the universality classes of critical points in 1 + 1dimensions with the Lorentz and SU(2) symmetry. We can also identify the level k = 0 with thegapped state with a unique “disordered” ground state. In the presence of the SU(2) and a certaindiscrete Z2 symmetry of the WZW theory, which corresponds to the translation symmetry ofthe spin chain, we find that a renormalization-group (RG) flow is possible between SU(2)k andSU(2)k0 WZW theories only if k ⌘ k0 mod2. That is, the gapless critical phases in 1+1 dimensionwith the SU(2), the Z2, and the Lorentz symmetries are classified into the two “symmetry-protected” categories: one corresponds to even levels and the other to odd levels. In terms ofspin chain models, as long as the SU(2) spin-rotation and the lattice translation symmetries areunbroken (either explicitly or spontaneously), a spin chain with an integer S can only realizeSU(2)k WZW theory with an even k, while one with a half-odd-integer S can only realize SU(2)kWZW theory with an odd k [3].

References[1] Z.-C. Gu and X.-G. Wen, Phys. Rev. B 80, 155131 (2009); F. Pollmann, E. Berg, A. M.Turner, and M. O., Phys. Rev. B 85 , 075125 (2012).[2] S. Ryu and S.-C. Zhang, Phys. Rev. B 85, 245132 (2012); O. M. Sule, X. Chen, and S. Ryu,Phys. Rev. B 88, 075125 (2013); C.-T. Hsieh, O. M. Sule, G. Y. Cho, S. Ryu, and R. G. Leigh,Phys. Rev. B 90, 165134 (2014).[3] S. C. Furuya and M. O., in preparation

Correlation E↵ects on the Topological Edge States in Graphene Nanoflakes:Relation between Nanostructure and Local Magnetic Order

T. Kariyado1, D. Seki,1 and Y. Hatsugai1

1Division of Physics, University of Tsukuba, Tennodai 1-1-1, Tsukuba 305-8571, Japan

At the zigzag edge of graphene, topologically protected edge states appear [1,2]. Correlatione↵ects on this edge states are important since they form a flat band in the momentum space,which is prone to exhibits magnetic[1,3] or possibly some other kinds of order.

In this study, graphene nanoflakes with zigzag edges are theoretically studied focusing onthe correlation e↵ects on the edge states. A nanoflake is suitable to study relation betweennanostructures and correlation e↵ects. We first show that it is possible to have insights into edgestates by constructing given flakes by cutting and pasting triangle flakes. A triangle flake withzigzag edges is an ideal “building block” since it has exact zero energy edge states. In numerics,the “cut and paste” is implemented as an adiabatic change of selected transfer integrals. Byfollowing the evolution of the energy levels and wave functions against this adiabatic change,insights on the edge states can be extracted. For instance, the suppression of the weight of edgestate wave function at a 120� corner [4] can be understood by cutting a triangle. Similarly, 240�

and 300� corners, are also investigated and it is shown that the edge states decrease at thesecorners. As a further application, we connect a shift in bulk Dirac cones caused by uniaxialstrain and anisotoropy of the strained triangle flake by making graphene ribbon with triangles.

When the chiral symmetry exists, it sometimes becomes easy to handle correlation e↵ects.That is, when the energy of the bulk states is far away from the zero energy edge states,it is possible to obtain an well approximated ground state wave function with the help of apseudopotential by the chiral basis [5,6]. In some cases, including the case with the trinangleflake, the bulk states of nanoflakes have sizable gaps by finite size e↵ect, and the idea becomesapplicable. Then, we calculate the local spin moment induced by correlation using the obtainedwave function. It is found that decrease of edge state at the corner has direct relevance tosuppression of the local spin moment at the corner. Spatial resolution of the magnetic momentis beyond the Lieb’s theorem for the total moment in chiral symmetric systems [7].

References[1] M. Fujita et al., J. Phys. Soc. Jpn. 65, 1920 (1996).[2] S. Ryu and Y. Hatsugai, Phys. Rev. Lett. 89, 077002 (2002).[3] S. Okada and A. Oshiyama, Phys. Rev. Lett. 87, 146803 (2001).[4] Y. Shimomura et al., J. Phys. Soc. Jpn. 80, 054710 (2011).[5] Y. Hatsugai et al., New J. Phys. 15, 035023 (2013).[6] Y. Hamamoto et al., Phys. Rev. B 88, 195141 (2013).[7] E. H. Lieb, Phys. Rev. Lett. 62, 1201 (1989).

The Mott insulator Ca2RuO4 in a non-equilibrium steady state

I. Terasaki1

1Department of Physics, Nagoya University, Nagoya 464-8602, Japan

The non-equilibrium steady state (NESS) is a steady state with constant flows of particle andenergy. Obviously, it is the simplest system for non-equilibrium states, and many researchershave expected that the thermodynamics and statistical physics are able to be upgraded toinclude NESS. However, still missing is a real substance that exhibits essentially non-equilibriumcharacteristics.

Non-ohmic conduction is a typical example for NESS, and in particular we have focused onnonlinear conduction in strongly correlated electrons. As is generally agreed, strong correlationis a fertile source of electronic phase transitions such as high-temperature superconductivity incopper oxides, colossal magnetoresistance in manganese oxides, and multipole ordered statesin heavy fermion intermetallics. Since some of such ordered states are susceptible to externalimpetus, we have searched for an ordered state susceptible to external electric field.

We have eventually arrived at the Mott insulator Ca2RuO4; this particular oxide undergoesa metal-insulator transition at around 360 K, and a low external pressure easily breaks the low-temperature insulating state. Nakamura et al. [1] have recently discovered a small electric fieldalso breaks the insulating state. By controlling the sample temperature using black body radi-ation [2], we have observed the Seebeck coe!cient in various external currents simultaneously.The resistivity decreases with increasing current density, and the Seebeck coe!cient is signifi-cantly enhanced by 50-100 µV/K, which cannot be ascribed to a simple self heating. We havefurther found that the volume is changed with external current density in isothermal conditions.

In the present talk, we will show various anomalous properties of Ca2RuO4 in the nonlinearconduction regime, and compare them with those of other materials.

The author would like to thank R. Okazaki, Y. Nishina, Y. Yasui, H. Taniguchi and F.Nakamura for collaboration. This work was partially supported by a Grant-in-Aid for ScientificResearch from MEXT, Japan (26247060).

References[1] F. Nakamura et al.: Sci. Rep. 3 (2013) 2536.[2] R. Okazaki et al.: J. Phys. Soc. Jpn 82 (2013) 103702.

Hydrogen-bonded Purely Organic Conductors: Exploration of Hydrogen-bond-dynamics-coupled Electronic Properties

A. Ueda

The Institute for Solid State Physics, The University of Tokyo, Kashiwanoha 5-1-5, Kashiwa, Chiba 277-8581

Hydrogen-bonded (H-bonded) organic conductors have attracted continuous attention because they show unique molecular arrangements, packing structures, and electronic (or electrostatic) features in-trinsically due to the H-bond formation, resulting in various kinds of interesting physical properties and functionalities [1]. In these studies, the “static”  effects  of  the  H-bond are frequently used to con-trol or regulate the crystal and electronic structures, however, the  “dynamic”  effects, such as proton (or hydrogen atom) transfer within the H-bond, on the electronic properties are little investigated.

We recently synthesized a new type of H-bonded purely organic conductor, -H3(Cat-EDT-TTF)2 (-H) [2], in which the conducting layers, composed of the Cat-EDT-TTF+0.5 molecules, are directly connected by [O·· ·H···O]–1 H-bonds (Figure 1). This peculiar crystal structure, intrinsically different from that of the previous systems [1], has offered us an opportunity to explore novel electronic fea-tures and physical properties related to H-bond dynamics. In this presentation, I will firstly introduce the structure and properties of -H with a quantum spin liquid ground state [2, 3], and then give a de-tailed description about the [O···D·· ·O]–1 deuterated analogue, -D3(Cat-EDT-TTF)2 (-D), showing an unprecedented charge-order phase transition coupled to the H-bond dynamics [4], in terms of the H/D isotope and pressure effects.

This work was performed by collaboration with Mr. S. Yamada, Dr. T. Isono, Mr. H. Kamo, Prof.

H. Mori (ISSP, The Univ. of Tokyo), Dr. A. Nakao (CROSS), Prof. R. Kumai, Prof. H. Nakao, Prof. Y. Murakami (KEK), Prof. K. Yamamoto (Okayama Univ. of Sci.), Prof Y. Nishio (Toho Univ.), and Prof. S. Uji (NIMS).

Figure 1: Crystal packing of -H and -D. References [1] M. Fourmigué et al.: Chem. Rev. 104 (2004) 5379. [2] T. Isono et al.: Nat. Commun. 4 (2013) 1344. [2] T. Isono et al.: Phys. Rev. Lett. 112 (2014) 177201. [3] A. Ueda et al.: J. Am. Chem. Soc. 136 (2014) 12184.

Semi-classical spin dynamics of the antiferromagnetic Heisenberg model onthe kagome lattice

M. Taillefumier1, Julien Robert2, Christopher Henley3, Roderich Moessner4, andBenjamin Canals2

1Okinawa Institute of sciences and technologies, 1919-1 Tancha-son, Okinawa 904-0495 Japan2Institut Neel, CNRS/UJF, 25 avenue des Martyrs, BP 166, 38042 Grenoble, Cedex 09, France

3LASSP, Clark Hall, Cornell University, Ithaca, NY 14853-2501, USA4Max Planck Institute for complex systems, Noethnitzer Str. 38 D-01187 Dresden, Germany

We investigate the dynamical properties of the classical antiferromagnetic Heisenberg modelon the kagome lattice using a combination of Monte Carlo and molecular dynamics simulations.We find that frustration induces a distribution of timescales in the cooperative paramagneticregime (i.e. far above the onset of coplanarity), as recently reported experimentally in deuteriumjarosite. At lower temperature, when the coplanar correlations are well established, we show thatthe weathervane loop fluctuations control the system relaxation: the time distribution observedat higher temperatures splits into two distinct timescales associated with fluctuations in the planeand out of the plane of coplanarity. The temperature and wave vector dependences of these twocomponents are qualitatively consistent with loops di↵using in the entropically dominated freeenergy landscape. Numerical results are discussed and compared with the O(N) model andrecent experiments for both classical and quantum realizations of the kagome magnets.

ReferencesMathieu Taillefumier, Julien Robert, Christopher L. Henley, Roderich Moessner, and BenjaminCanals, Phys. Rev. B 90, 064419 (2014)

Emergent collective excitations and anomalous dynamics of spin ice withshort-range interaction

M. Udagawa1, L. D. C. Jaubert2, C. Castelnovo3 and R. Moessner4

1Department of Applied Physics, University of Tokyo, Hongo 7-3-1, Bunkyo, Tokyo 113-86562. Okinawa Institute of Science and Technology, Onna-son, Okinawa 904-0412, Japan

3. TCM group, Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, United Kingdom

4. Max Planck Institute for the Physics of Complex Systems, Nothnitzer Str. 38, D-01187 Dresden,

Germany

Spin ice is a prototypical frustrated magnet, with a number of remarkable features, suchas ground-state degeneracy, fractional excitations, and quasi-long range correlation, which nowserve as fundamental concepts to understand frustrated magnetism. Among these properties,we focus on the dynamical character of spin ice. Indeed, Ho(Dy)2Ti2O7, a canonical examples ofdipolar spin ice system, exhibits several anomaly in its dynamics. It shows a drastic divergence ofrelaxation time at low temperatures [1, 2], and the role of monopole excitations in this extremelyslow dynamics has been intensively discussed [3, 4]. Dynamical anomalies have also been foundin several variants of spin ice. For example, in Pr2Ir2O7, a metallic spin ice system, so-calledspontaneous Hall e!ect has been observed [5], in possible relation to the slow dynamics of itscompound at low temperatures.

In this contribution, we study the classical dynamics of J1-J2-J3 spin ice model. This modelis the simplest extension of the nearest-neighbor spin ice, and also captures the essential partof the metallic spin ice system, where conduction electrons interact with spin ice. Remarkably,this model can be mapped to the monopole gas model with the nearest-neighbor interaction ondual diamond lattice, if J2 = J3 ! J is satisfied [6], and gives an idealistic test ground to studythe e!ects of monopole interactions on dynamical properties.

We analyzed the classical dynamics of this model with a waiting-time Monte Carlo method,and clarified the time evolution of monopole density and magnetization for all the range ofJ . In particular, we found several quasi-stable macroscopic states survive as a steady statewith macroscopically long relaxation time, even though they have higher energy compared withground state. In this contribution, we will describe the nature of these steady states. In partic-ular, we discuss the possible relation between the emergent collective excitation which we term“monopole jellyfish” and the spontaneous Hall e!ect observed in Pr2Ir2O7 [7].

References[1] K. Matsuhira, Y. Hinatsu, and T. Sakakibara, J. Phys. Condens. Matter 13, L737 (2001).[2] J. Snyder et al., Phys. Rev. B 69, 064414 (2004).[3] L. D. C. Jaubert and P. C. W. Holdsworth, J. Phys.: Condens. Matter 23, 164222 (2011).[4] C. Castelnovo, R. Moessner and S. L. Sondhi, Phys. Rev. Lett. 104, 107201 (2010).[5] Y. Machida et al., Nature 463, 210 (2010).[6] H. Ishizuka and Y. Motome, Phys. Rev. B 88, 100402(R) (2013)[7] M. Udagawa, L. Jaubert, C. Castelnovo and R. Moessner, in preparation.

Emergent critical phase in a correlated electron system Yosuke Matsumoto, Takahiro  Tomita,  Kentaro  Kuga,  Eoin  C.  T.  O’Farrell,  

Yasuyuki Shimura and Satoru Nakatsuji

Institute for Solid State Physics, University of Tokyo, Kashiwanoha 5-1-5, Kashiwa, Chiba 277-8581

In this talk, I would like to discuss the novel quantum criticality (QC) recently observed in the valence fluctuating YbAlB4 systems. So far, QC in heavy fermion systems has been studied mainly for Kondo lattice systems with integer valence, where a quantum critical point is usually expected to be on the border of magnetism. On the other hand, the first Yb-based heavy fermion superconductor -YbAlB4 provides a unique example of QC in the mixed valent compounds [1, 2, 3, 4]. In addition, the QC cannot be explained by the standard spin fluctuation mechanism and emerges without tuning any con-trol parameter, indicating formation of a strange metal phase [4]. Recent resistivity measurements un-der pressure have revealed that a non-Fermi liquid phase is stable over a finite pressure range up to ~ 0.4 GPa [5], which supports this idea. Here we review such novel phenomena observed in -YbAlB4 as well as those found in its isostructural polymorph -YbAlB4 discussing a possible role of valence fluctuation and anisotropic hybridization. In particular, we will discuss a sharp valence crossover in-duced by a chemical substitution in -YbAlB4 where we found a pronounced NFL behavior as a pos-sible evidence of a quantum valence criticality [6]. These works have been done in collaboration with P. Coleman, A. H. Nevidomskyy, T. Sakakibara, Y. Uwatoko, Y. Karaki, K. Sone, J. Hong, S. Suzuki, H. Cao, D. MacLaughin, M. Okawa, Y. Takata, M. Matsunami, R. Eguchi, M. Taguchi, A Chainani, S. Shin, Y. Nishino, K. Tamasaku, M. Yabashi, T. Ishikawa, Y. Kiuchi, D. Hamane, M. Isobe, M. Koike. We thank them for their contributions.

References

[1] S. Nakatsuji, K. Kuga, Y. Machida, T. Tayama, T. Sakakibara, Y. Karaki, H. Ishimoto, E. Pearson,

G. G. Lonzarich, H. Lee, L. Balicas, and Z. Fisk, Nature Phys. 4 (2008) 603. [2] K. Kuga, Y. Karaki, Y. Matsumoto, Y. Machida, and S. Nakatsuji, Phys. Rev. Lett. 101 (2008)

137004. [3] M. Okawa, M. Matsunami, K. Ishizaka, R. Eguchi, M. Taguchi, A. Chainani, Y. Takata, M. Yaba-

shi, K. Tamasaku, Y. Nishino, T. Ishikawa, K. Kuga, N. Horie, S. Nakatsuji, and S. Shin, Phys. Rev. Lett. 104 (2010) 247201.

[4] Yosuke Matsumoto, Satoru Nakatsuji, Kentaro Kuga, Yoshitomo Karaki, Naoki Horie, Yasuyuki Shimura, Toshiro Sakakibara, Andriy H. Nevidomskyy, Piers Coleman, Science 331 (2011) 316.

[5] T. Tomita, K. Kuga, Y. Uwatoko, P. Coleman, and S. Nakatsuji, preprint (2015). [6] K. Kuga et al., preprint (2015).

Classification of two-dimensional

symmetry protected topological phases with a reflection symmetry T. Yoshida,1 T. Morimoto,1 and A. Furusaki.1

1Condensed Matter Theory Laboratory, RIKEN, Hirosawa 2-1, Wako, Saitama 361-0198

After discovery of a topological crystalline insulator in SnTe[1,2], it became clear that spatial symmetries can protect topological structures. As well as this new phase, realization of topological phases is reported not only for free-fermion systems but also for correlated systems including spin and bosonic systems. Such phases are called as symmetry protected topological (SPT) phases. Employing a classification scheme based on the Chern-Simons theory[3,4], we classify SPT phases protected by a reflection symmetry. Besides, we propose a spin model which shows nontrivial phase protected by the reflection symmetry[5]. This is a bosonic extension of topological crystalline insulators. In study of femionic systems, we elucidate that correlation effects can reduce topological classification; topologi-cal classes in free fermion systems are reduced into those of ZN in the presence of a local discrete symmetry. Here, N denotes order of the local symmetry.

References:

[1] L. Fu: Phys. Rev. Lett. 106, (2011) 106802. [2] T. H. Hsieh et al.: Nat. commun. 3, (2012) 982. [3] Y.-M. Lu and A. Vishwanath: Phys. Rev. B 86, (2012) 125119. [4] C.-T. Hsieh et al.: arXiv:1406.0307 (2014). [5] T. Yoshida et al.; in preparation.

Quantum Fluctuations in Exchange-Based Spin Ice Pr2Zr2O7 K. Kimura,1 S. Nakatsuji,2 J.-J. Wen,3 C. Broholm,3,4,5 M. B. Stone,5 Y. Shimura,2 T. Sa-

kakibara,2 H. Takeda,2 M. Takigawa,2 Y. Karaki,6 K. Sugawara,7 E. Nishibori,7 and H. Sawa7

1Department of Materials Engineering Science, Osaka University, Machikaneyama 1-3, Toyonaka, Osaka 560-8531, Japan

2Institute for Solid State Physics, University of Tokyo, Kashiwanoha 5-1-5, Kashiwa, Chiba 277-8581, Japan 3Institute for Quantum Matter and Department of Physics and Astronomy, Johns Hopkins University, Baltimore,

Maryland 21218, USA 4NIST Center for Neutron Research, NIST, Gaithersburg, Maryland 20899, USA

5Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA 6Faculty of Education, University of the Ryukyus, Nishihara, Okinawa 903-0213, Japan

7Department of Applied Physics, Nagoya University, Furo-Cho, Chikosa, Nagoya 464-8603, Japan

Spin ice on pyrochlore lattice is a prototypical example of frustrated magnetism in which dipolar in-teractions between classical spins stabilize a frozen constrained state [1]. Remarkably, it exhibits a finite residual entropy resembling to the disordered proton configuration of water ice as well as emer-gent magnetic monopolar quasi-particles [2]. Recently, introducing quantum fluctuations into spin ice has attracted considerable interest because of the possible realization of novel quantum states, such as quantum spin liquid that exhibits quantum version of magnetic monopoles.

In this talk, we will present our recent results on a new class of spin ice material Pr2Zr2O7, where spin correlations are provided by quantum mechanical superexchange interactions rather than classical dipolar interactions [3,4]. Similarly to conventional spin ice, magnetic susceptibility and specific heat show activated dynamics. Pinch-point features in quasi-elastic diffuse neutron scattering reflects ad-herence to a divergence free local constraint for disordered spins on long time scales. In sharp contrast to conventional ice, however, more than 90% of the neutron scattering is inelastic and devoid of pinch points furnishing evidence for magnetic monopolar quantum fluctuations. We will also present results of low-temperature properties under a magnetic field as well as systematic study on the relationship between low-temperature properties and sample quality.

References

[1] S. T. Bramwell and M. J. P. Gingras, Science 294, 5546 (2001). [2] C. Castelnovo, R. Moessner, and S. L. Sondhi, Nature 451, 42 (2008). [3] K. Kimura, S. Nakatsuji, J.-J. Wen, C. Broholm, M. B. Stone, E. Nishibori, H. Sawa, Nat. Commun. 4, 1934 (2013). [4] K. Kimura and S. Nakatsuji, JPS Conf. Proc. 3, 014027 (2014).

Magnetic monopoles in diluted quantum spin ice

Olga Petrova1, Roderich Moessner,1 and S. L. Sondhi1,2

1Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany

2Department of Physics, Princeton University, Princeton, NJ 08544, USA

Quantum spin ice is a topic of much current interest, stemming from its promise as a topolog-ical spin liquid in 3d, as well as recent discoveries of candidate compounds. However, preciselywhat signatures to look for to nail down quantum behavior in the spin ices is not clear. Inthis talk I will show that the most visible place to look for quantum e↵ects in spin ice is inthe presence of emergent magnetic monopoles, whose fractionalized nature is perhaps the moststriking feature of this system.

Our focus is on the case of weakly diluted quantum spin ice, where we find the emergenceof hydrogenic excited states, resembling those in doped semiconductors, in which a magneticmonopole is bound to a vacancy at various distances. We obtain an approximate expressionfor the dynamic neutron scattering structure factor [1] via a mapping to an e↵ective exactlysolvable model defined on the Bethe lattice.

References[1] O. Petrova, R. Moessner, S. L. Sondhi, arXiv:1501.02445.

Dynamics of coupled electrons, skrymions and monopoles N. Nagaosa1,2

1RIKEN Center for Emergent Matter Science (CEMS), Hirosawa 2-1, Wako, Saitama 361-0198 2Department of Applied Physics, University of Tokyo, Hongo 7-3-1, Bunkyo-ku Tokyo 113-8656

A swirling spin texture in magnets, skyrmion, is an emergent topological particle recently discov-

ered in several chiral magnets, and is now recognized as a promising candidate for the information

carrier in magnetic memories [1]. Furthermore, the creation (termination) point of a skyrmion corre-

sponds to the monopole (anti-monopole) in three dimensional systems. The conduction electrons cou-

pled to these topological spin textures show rich behaviors distinct from those in other situations.

We theoretically study the coupled dynamics of this system in terms of the numerical solution of

Landau-Lifshitz-Gilbert equation, first-principles band structure calculations, and field theoretical

methods. The topics include the quantized anomalous Hall effect in skyrmion crystal, resistivity in-

duced by the monopole fluctuation, and current-driven motion of skyrmions.

Collaborators of these works are J. Iwasaki, W. Koshibae, Aron Beekman, M. Mostovoy, J.D.

Zang, M. Mochizuki, J. H. Park, J. H. Han, C. Schuette, A. Rosch, X. Z. Yu, Y. Matsui, Y. Onose, N.

Kanazawa, T. Ideue, Y. Shiomi, Y. Taguchi, and Y. Tokura. References

[1] N. Nagaosa and Y. Tokura, Nature Nanotechnology 8, 899 (2013).

Light-induced Higgs-mode resonance in s-wave and d-wave superconductors

N. Tsuji

Department of Physics, University of Tokyo, Hongo 7-3-1, Bunkyo-ku Tokyo 113-0033, Japan

Collective modes of the order parameter inherent in superconductors are classified into two:the phase and amplitude modes. The former corresponds to the Nambu-Goldstone (NG) mode,while the latter is often called the Higgs mode, in analogy with the recently discovered Higgsparticle in high-energy physics. In superconductors, the NG mode is pushed to high energy (!plasma frequency) due to the Anderson-Higgs mechanism, whereas the Higgs mode remains toexist in the low-energy regime. The extended BCS theory predicts that the Higgs-mode energyis given by 2! (i.e., the superconducting gap), so that the Higgs mode is the lowest energyexcitation degenerate to the bottom energy of quasiparticle excitations. Since the Higgs modeis a scalar-boson excitation without being accompanied by quantum numbers such as electriccharge, magnetic moment, etc., it has been di"cult to excite and detect the Higgs mode byexternal perturbations in experiments.

Here we present how the Higgs mode can be coherently excited by strong laser fields for boths-wave and d-wave superconductors. For s-wave superconductors, we employ the Bogoliubov-deGennes (BdG) equation and nonequilibrium dynamical mean-field theory [1] to show that an acelectric field with frequency # should induce a collective amplitude oscillation of the order pa-rameter with a frequency 2# via the nonlinear light-matter coupling [2]. The induced oscillationturns out to become “resonant” with the Higgs mode when the resonance condition 2# = 2!is satisfied. This results in a giant third-harmonic generation (THG). One can distinguish theHiggs-mode resonance from quasiparticle excitations at the band-edge singularity by looking atthe peak structure of the THG susceptibility. These phenomena have been recently observed ina THz laser experiment [3] in nice agreement with the theory. For d-wave superconductors, wecalculate the susceptibility for the order-parameter oscillation induced by the ac field based onthe mean-field theory, and find that the Higgs-mode resonance appears as a broad peak with 2#slightly smaller than |2!(k = (!, 0))|. This can be understood from the fact that the pairinginteraction peaked at the antinode contributes to the Higgs-mode resonance.

References[1] H. Aoki, N. Tsuji, et al., Rev. Mod. Phys. 86, 779 (2014).[2] N. Tsuji and H. Aoki, arXiv:1404.2711.[3] R. Matsunaga, N. Tsuji, et al., Science 345, 1145 (2014).

Solidifying a Quantum Spin Liquid in a 3D Toric Code Y. Kamiya,1 Y. Kato,2 J. Nasu,3 M. Udagawa,4 and Y. Motome4

1iTHES and Condensed Matter Theory Laboratory, RIKEN, Hirosawa 2-1, Wako, Saitama 351-0198, Japan 2RIKEN Center for Emergent Matter Science (CEMS), Hirosawa 2-1, Wako, Saitama 351-0198, Japan

3Department of Physics, Tokyo Institute of Technology, Ookayama 2-12-1, Meguro, Tokyo 152-8551, Japan 4Department of Applied Physics, University of Tokyo, Hongo 7-3-1, Bunkyo, Tokyo 113-8656, Japan

While some extremely frustrated magnets may realize quantum spin liquids (QSLs), proposed frus-trated quantum Hamiltonians are very difficult to deal with, and it is by no means easy to obtain con-clusive evidence. On the other hand, a series of models such as the Kitaev model [1] and its extensions are useful in examining generic properties of QSLs, because it can be rigorously shown that their ground states are QSLs and moreover perturbative as well as thermal effects can be investigated at a quantitative level by using numerical methods. In this talk, I will present the thermodynamic phase di-agram of a 3D toric code perturbed by ferromagnetic Ising interaction obtained by quantum Monte Carlo simulations. The interaction introduces quantum fluctuations to the loop-type “magnetic flux” excitations, which are confined at low temperature and responsible for stabilizing a QSL phase at finite temperature [2]. At a large enough value of this coupling, the interaction eventually “solidifies” the spin liquid into a magnetic ordered state breaking global Z2 symmetry. We find that the critical tem-perature to the QSL phase is almost insensitive to the magnitude of the Ising coupling and also that the transition between the QSL and long-range ordered phases is strongly discontinuous. Near and inside the topological phase, we use the directed-loop algorithm supplemented by what we call “fictitious vertices,” with which the multi-spin off-diagonal terms can be treated very efficiently. References [1] A. Y. Kitaev, Ann. Phys. (N.Y.) 303, 2 (2003); A. Y. Kitaev, Ann. Phys. (N.Y.) 321, 2 (2006). [2] C. Castelnovo and C. Chamon, Phys. Rev. B 78, 155120 (2008).

Dynamics of Quantum Spin-Liquids

D. Kovrizhin

1, J. Knolle,

1, J. T. Chalker,

2and R. Moessner

3

1T.C.M. Group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom2Theoretical Physics, Oxford University, 1, Keble Road, Oxford OX1 3NP, United Kingdom

3Max Planck Institute for the Physics of Complex Systems, D-01187 Dresden, Germany

We provide a complete and exact theoretical study of the dynamical structure factor of a two-dimensional quantum spin liquid in gapless and gapped phases, as realized in Kitaevs honeycombmodel. We show that there are direct signatures – qualitative and quantitative – of the Majoranafermions and gauge fluxes emerging in this model. These include counterintuitive manifestationsof quantum number fractionalization, such as a neutron scattering response with a gap evenin the presence of gapless excitations, and a sharp component despite the fractionalizationof electron spin. Our analysis identifies new varieties of the venerable x-ray edge problemand explores connections to the physics of quantum quenches. I will present the results forthe structure factor in 2D Kitaev honeycomb model and in its 3D (hyperhoneycomb lattice)generalization [3].

Figure 1: Dynamic structure factor in thegapped QSL phase of a 2D Kitaev honeycombmodel on a logarithmic color scale [1] as a func-tion of ! along the cut M�KM in the Brillouinzone. Remarkably the structure factor shows asharp �-function response (red bar at the bot-tom).

References

[1] J. Knolle, D. L. Kovrizhin, J. T. Chalker, and R. Moessner, “Dynamics of a Two-DimensionalQuantum Spin Liquid: Signatures of Emergent Majorana Fermions and Fluxes”, Phys. Rev. Lett. 112,207203 (2014).[2] J. Knolle, Gia-Wei Chern, D. L. Kovrizhin, R. Moessner, and N. B. Perkins, “Raman Scatter-ing Signatures of Kitaev Spin Liquids in A2IrO3 Iridates with A=Na or Li”, Phys. Rev. Lett.113,187201 (2014).[3] J. Knolle, D. L. Kovrizhin, paper in preparation

Poster� �Presentations�

Periodically-driven Kondo impurity coupled to an ultracold fermionic bath

K. Iwahori, N. Kawakami

Department of Physics, Kyoto University

The dynamics of a single impurity coupled to a fermionic or bosonic bath is one of the fun-damental problems in condensed matter physics, and plays an important role in the polaronicsystems, X-ray absorption problem, Kondo e!ect and so on. Recently, these impurity problemsare studied in the ultracold atomic systems [1, 2, 3]. By utilizing their high controllability,nonequilibrium dynamics of impurity is also studied; for example, space- and time-resolvedobservation of a mobile spin impurity in a one-dimensional lattice system [3], Orthogonal Catas-trophe by the radio-frequency field [4], and periodically driven spin-boson model [5].

In this paper, we study the periodically-driven impurity spin dynamics coupled to an ul-tracold fermionic bath by the Kondo exchange coupling. The time-dependent Hamiltonian weconsider here is given by

H(t) = HBath + JzSzsz(0) + J!(t)(S

+!†"(0)!#(0) + h.c) + h(t)Sz (1)

where HBath describes a one-dimensional fermionic bath, whose spin sz(x) at x = 0 is coupledto the impurity spin Sz via the anisotropic Kondo coupling Jz and J!(t). The time-dependentlocal magnetic field is denoted by h(t).

In general, even in the noninteracting case, it is di"cult to solve the dynamics of the peri-odically driven quantum system analytically. Thus we consider the case that the external fieldchanges its values discretely in time and the Hamiltonian is at the special point in the param-eter space (Toulouse limit) at which we can solve each time-step analytically and thereby treatthe full dynamics exactly. Then, taking the continuum limit, we obtain a solution precisely forarbitrary time-periodic external fields.

We calculate the expectation values of the impurity spin and the magnetization of bathfermions in several di!erent cases: (i) h(t) has a rectangular-type time-dependence and J!(t) istime-independent, (ii) h(t) has a sinusoidal time-dependence which is discretized appropriatelyand J!(t) is time-independent. As a result, we find that their characteristic behavior changesdramatically with the field-intensity h, the field-frequency #, and the Kondo temperature TK .In h ! #, TK , they oscillate with the frequency of h, while in # ! h, TK , they approach atemporally constant value.

References[1] A.Schirotzek et al.: Phys. Rev. Lett. 102, 230402 (2009).[2] J.Bauer et al.: Phys. Rev. Lett. 111, 215304 (2013).[3] T.Fukuhara et al.: Nature Phys. 9, 235 (2013)[4] M.Knap et al.: Phys. Rev. Lett. 111, 265302 (2013).[5] M.Knap et al.: Phys. Rev. X 2, 041020 (2012).

PS-01

Photo-Induced Kondo Effect and its Anomalous Behavior M. Nakagawa and N. Kawakami

Department of Physics, Kyoto University, Kitashirakawa, Sakyo-ku, Kyoto 606-8502

Kondo effect is a ubiquitous phenomenon in condensed matter physics. It plays a key role in many systems such as heavy-fermion materials, leading to plethora of intriguing quantum phenomena. In this presentation, we propose a novel route to induce the Kondo effect, using external laser excitation. Naturally, it is tightly connected to non-equilibrium physics in condensed matter. We discuss here the realization scheme of the photo-induced Kondo effect, and its anomalous properties in the non- equilibrium steady state. Our scheme is motivated by recent development of manipulation techniques in ultracold atomic gases [1-4]. Using ultracold fermions with two orbitals and optical transition between them, effective hy-bridization between orbitals is induced, which results in the emergence of the Kondo effect. The heavy-fermion liquid realized by the laser shows intriguing behavior, since the laser field strongly couples with the spin degrees of freedom. We demonstrate that the laser-induced Kondo state leads to component-selective renormalization of effective masses, and also show that novel competition with other Kondo screening channels drives a photo-induced "switch" of the Kondo effect. [1] A. V. Gorshkov et al., Nat. Phys. 6, 289 (2010). [2] G. Cappellini et al., Phys. Rev. Lett. 113, 120402 (2014). [3] F. Scazza et al., Nat. Phys. 10, 779 (2014). [4] X. Zhang et al., Science 345, 1467 (2014).

PS-02

Transport properties for a quantum dot coupled to normal leads with thepseudogap structure

Bunpei Hara,1 Akihisa Koga,1 and Tomosuke Aono2

1Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan2Department of Electrical and Electronic Engineering, Ibaraki University, Ibaraki 316-8511, Japan

Magnetic impurity problems in d-wave superconductors or Dirac fermions have been dis-cussed in the context of the pseudogap Kondo problem [1,2]. Recently, quantum dot systemscoupled to normal leads with the pseudogap structure have attracted much attention [3]. Inthe equilibrium system, the competition between the Kondo and local moment states has beendiscussed in detail [1,2]. By contrast, in the non-equilibrium system with a finite voltage, thesystematic analysis is lacking, and thereby it is necessary to study how the pseudogap structurea!ects the transport properties in the quantum dot system.

In this study, we consider a symmetric pseudogap Anderson impurity model as

H =!

!

!dnd! +!

k!"

(!k ! µ")nk!" + Und!nd" +!

k!"

"vc†k!"d! +H.c.

#, (1)

where ck!" is the annihilation operator of an electron with wave number k and spin "(=", #)in the #th lead, and nk!" = c†k!"ck!". d! is the annihilation operator of an electron at the

quantum dot, n! = d†!d!. !k is the dispersion relation of the lead and v is the hybridizationbetween the lead and quantum dot. $d and U are the energy level and Coulomb interaction atthe quantum dot. To discuss how the pseudogap structure a!ects steady state properties, weconsider the density of states for both leads %"(&) = %0|&|r, where r is the pseudogap parameter.We then set the chemical potentials as µ1 = V/2 and µ2 = !V/2, where V is the bias voltage.Applying the second-order perturbation theory [4,5] to the model, we clarify that the pseudogapstructure in the normal leads induces the cusp structure in the density of states, in addition tothe Coulomb peaks. The r-dependence of the conductance is also addressed.

References

[1] D. Witho! and E. Fradkin, Phys. Rev. Lett. 64 1835 (1990).[2] C. Gonzalez-Buxton and K. Ingersent, Phys. Rev. B. 57 14254 (1998).[3] C.-H. Chung and K. Zhang, Phys. Rev. B. 85 195106 (2012).[4] K. Yosida and K. Yamada, Prog. Theor. Phys. Suppl. 46 244 (1970).[5] S. Hershfield, J. Davies, and J. Wilkins, Phys. Rev. B. 46 7046 (1992).

PS-03

Dynamical mean-field analysis of non-equilibrium relaxation processes in an electron-phonon coupled system

Y. Murakami,1 P. Werner,2 N. Tsuji,1 and H. Aoki1

1Department of Physics, University of Tokyo, Hongo 7-3-1, Bunkyo-ku Tokyo 113-8656 2Department of Physics, University of Fribourg, Fribourg, Switzerland

The non-equilibrium properties of correlated systems have recently attracted a lot of interest because

of cold-atom and pump-probe experiments. In the non-equilibrium dynamics of solids, elec-

tron-phonon (e-ph) interactions are expected to play an important role. From a microscopic and theo-

retical point of view, fundamental properties of electron-phonon systems can be captured by the sim-

ple Holstein model. However, many non-equilibrium properties of this model have yet to be revealed.

Here, in order to obtain new insights of non-equilibrium physics in e-ph systems, we investigate the

Holstein model both in the normal and superconducting states with the non-equilibrium dynamical

mean-field theory (DMFT) [1].

In the normal state and in the weak-coupling regime, a crossover from electron- to pho-

non-dominated relaxation is observed when the electron-phonon coupling is changed [2]. Namely, in

the weaker-coupling regime, oscillations in physical quantities decay before the momentum distribu-

tion of the electrons approaches its thermal value, while in the stronger-coupling regime, the electron

momentum distribution approaches a thermal value before the oscillations are damped. We show that

this crossover originates from the different dependence of the electron and phonon self-energies on the

e-ph coupling.

In the superconducting state [3], both the phonon mode and the collective amplitude (Higgs) mode of

the superconducting order parameter show up in the relaxation process. We reveal that the phonon

mode becomes long-lived when the e-ph coupling is sufficiently strong, which leads to qualitatively

different relaxation processes at weak and strong coupling. This behavior in the time domain turns out

to be related to properties of the spectral functions of electrons and phonons. We also discuss possibil-

ity of non-thermal critical points in this model, where the superconductivity is long-lived beyond its

phase boundary in equilibrium.

[1] H. Aoki et al., Rev. Mod. Phys. 86, 779 (2014).

[2] Y. Murakami, P. Werner, N. Tsuji and H. Aoki, Phys. Rev. B, 91, 045128 (2015). [3] Y. Murakami, P. Werner, N. Tsuji and H. Aoki, in preparation.

PS-04

Phase diagram of a one-dimensional generalized cluster model and dynamicsduring an interaction sweep

Takumi Ohta, Shu Tanaka, Ippei Danshita, and Keisuke Totsuka

Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan

We study quantum phase transitions and dynamical properties in the one-dimensional clustermodel with several interactions

HGC =N!

i=1

(!JXZX!xi !zi+1!

xi+2 + JY Y !yi !

yi+1 + JY ZY !yi !

zi+1!

yi+2) (1)

using exact diagonalization and infinite Time Evolving Block Decimation (iTEBD). First, theground-state phase diagram of the model is determined and each phase is characterized by orderparameters. We confirm that the degeneracy of the lowest levels in entanglement spectrumcorresponds to that of the ground state in the model with open boundary condition. Second,we investigate dynamical properties during an interaction sweep through the critical points ofthe model with open boundary condition using the time-dependent Bogoliubov transformation.After passing the critical point, a periodic structure in the length dependence of correlationfunctions and entanglement entropy is observed, which stems from the Bogoliubov excitationsgenerated near the critical points.

4 2 0 2 43

2

1

0

1

2

C*

C*

AF(x )

AF(y )

F(x )

F(y ) CJYZY

JYY

N N

- --

-

-

Figure 1: Phase diagram of the generalized cluster model(1) with JXZX = 1. The excitation gap vanishes on thesolid curves. C, C*, F, and AF represent cluster, dualcluster, ferromagnetic, and antiferromagnetic phases, re-spectively. The N phase cannot be characterized by stringand (anti) ferromagnetic order parameters. The super-script represents the direction of the order. Each phaseis determined by order parameters calculated with exactdiagonalization and iTEBD.

PS-05

Flux quench in the S = 1/2 XXZ chain

Yuya Nakagawa,1 Gregoire Misguich,2 and Masaki Oshikawa1

1Institute for Solid State Physics, University of Tokyo, Kashiwanoha 5-1-5, Kashiwa 277-8581, Japan2 Institut de Physique Theorique, CEA, IPhT, CNRS, URA 2306, F-91191 Gif-sur-Yvette, France

We study a flux quench problem in the spin-1/2 XXZ chain. The flux quench is a quantumquench where the flux ! piercing the XXZ chain is turned o! at t = 0 suddenly. If we formulatethe XXZ chain as a spinless fermion model, the flux ! corresponds to a vector potential on eachbond and this flux quench can be viewed as imposing a pulse (delta function) of electric field.Therefore some particle (or spin) current is generated in the system at t = 0. Recently thisquench was studied to illustrate the breakdown of the generalized Gibbs ensemble in integrablesystems [1]. Here, we focus on the time-evolution of the spin current after the quench andcalculate it numerically by the infinite time-evolving block decimation (iTEBD) method.

We find that the dynamics of the spin current depends strongly on the anisotropy parameter" of the XXZ chain and the amount of flux initially inserted. The long-time limit (t ! ") of thecurrent matches with predictions of linear response theory as the initial flux decreases, but thedeviation from linear response theory is largely a!ected by the sign of interactions. Furthermore,in some parameter region the current oscillates in time (Fig. 1, left panel) and the frequencyof the oscillation is proportional to |"|. Remarkably, the dynamics of momentum distributionof the spinless fermions reveals that this oscillation of the current is governed by excitationsdeep inside the shifted Fermi sea (Fig. 1, right panel). This mechanism of oscillations cannot becaptured by the e!ective Luttinger model corresponding to the microscopic XXZ chain, whichis in contrast with the previous studies on di!erent types of quench in the same model [2].

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 5 10 15 20 25 30

J(t)

t

! = - "/2#= -0.1

0.1-0.3

0.3-0.5

0.5

-0.80.8

-1.0

-1.2-1.5-2.0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

nq

Momentum q /!

"= -!/3, #= -0.5

t=0t=3t=5t=10t=15

0.14 0.16 0.18 0.2

0.22 0.24 0.26 0.28

0 5 10 15 20 25 30

t

J(t)

Figure 1: Left: Dynamics of the spin current after the quench. " is initial flux per site.

Anisotropy " is defined as HXXZ = #!

i

"Sxi S

xi+1 + Sy

i Syi+1 +"Sz

i Szi+1

#. Right: momentum

distribution of the spinless fermions. The dip (peak) structure deep inside the shifted Fermi seais observed (the inset shows the time-evolution of the current).

References[1] M. Mierzejewski, P. Prelovsek and T. Prosen: Phys. Rev. Lett. 113, 020602 (2014).[2] C. Karrasch et al.: Phys. Rev. Lett. 109, 126406 (2012), F. Pollmann, M. Haque andB. Dora: Phys. Rev. B 87, 041109(R) (2013).

PS-06

Topological Kondo insulators in strong laser fields

K. Takasan, M. Nakagawa, and N. Kawakami

Department of Physics, Kyoto University, Kyoto 606-8502, Japan

Controlling the nature of matter by laser light is an important topic in strongly correlated electron systems. We theoretically investigated how high-frequency laser field changes the nature of topological Kondo insulators. The topological Kondo insulator is a strongly correlated insulator that has a surface state protected by time-reversal symmetry (TRS) [1]. Recent theoretical and experimental studies suggest that SmB6 is a strong candidate for the topological Kondo insulator. By employing a prototypical model of the topological Kondo insulator [2], we treated the effect of laser field with the effective Floquet Hamiltonian, which gives the information of the system in the high-frequency limit. It enables us to map the time-periodic systems to static systems. We treated electron correlation effects by the slave-boson method, which allows us to calculate the renormalization effect self-consistently and thus determine the Kondo temperature. From the topological point of view, we showed how the laser light changes the topological phases of this system. We calculated the topological number at the mean field level and found how topological phase transitions occur according to laser intensity. Especially when the light is circularly polarized, TRS is broken. In that case we showed that the system is driven to a quantum Hall phase and a Weyl semi-metallic phase. In terms of the heavy fermion physics, we calculated the Kondo temperature as a function of laser light intensity and discussed the intensity-temperature phase diagram. Our calculation elucidated that there are the photo-induced hopping and the photo-induced hybridization under the laser irradiation, and that these photo-induced effects change the nature of the heavy electrons in the system quantitatively. Reference

[1] M. Dzero, K. Sun, V. Galitski, and P. Coleman. Phys. Rev. Lett. 104, 106408 (2010). [2] M. Tran, T. Takimoto, and K. Kim. Phys. Rev. B. 85, 125128 (2012).

PS-07

Effect of Ca-Doping on Pyrochlore Iridates Nd2Ir2O7 S. Maeda1, G. Goto1, T. Sakamoto1, M. Wakeshima2, Y. Hinatsu2,

A. Miyake3, M. Tokunaga3, and K. Matsuhira1

1 Graduate School of Engineering, Kyushu Institute of Technology, Kitakyushu 804-8550, Japan

2Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan 3Division of Chemistry, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan

Pyrochlore iridates Ln2Ir2O7 (Ln = Nd - Ho) exhibit metal-insulator transitions (MITs) [1, 2]. The 4f electrons from Ln3+ are well localized. As the (5d)5 electrons from Ir4+ form an unfilled t2g band, the 5d electrons contribute to the electrical conductivity. Their electrical conductivity and transition tempera-tures (TMI) depend on the ionic radius of Ln3+: the resistivity at room temperature and TMI increase with a reduction in the ionic radius. This fact means that the origin of MITs comes from Ir 5d electrons. In addition, these MITs involve an antiferromagnetic magnetic ordering of Ir moment with all-in/all-out arrangement [3-5]. Recent theoretical study predicts a new antiferromagnetic QCP around the disap-pearance of MIT [6]. In order to the criticality of this MIT, we have investigated the carrier doping ef-fect. In this presentation, we will report the Ca-doping effect in Nd2Ir2O7 (TMI =33 K). Figure 1 shows the electrical resistivity of (Na1-xCax)2Ir2O7. The MIT is rapidly suppressed with Ca-doping; TMI = 12 K for x = 0.05. Finally, the MIT disappears at x =0.15. We will also shows the experimental results of magnetization, specific heat, thermoelectric power, and high-field magnetoresistance effect in this presentation.

[1] K. Matsuhira, et. al.: J. Phys. Soc. Jpn. 76 (2007) 043706. [2] K. Matsuhira, et. al.: J. Phys. Soc. Jpn. 80 (2011) 094701. [3] K. Tomiyasu, et. al.: J. Phys. Soc. Jpn. 83 (2012) 034709. [4] H. Sagayama, et. al.: Phys. Rev. B 87 (2013) 100403(R). [5] H. Guo, et. al.: Phys. Rev. B 88 (2013) 060411(R). [6] L. Savary, et. al.: Phys. Rev. X 4 (2014) 041027.

1

10

100

103

104

105

0 50 100 150 200 250 300

ρ (mΩ

cm

)

T (K)

x=0

x=0.15

x=0.05

(Na1-xCax)2Ir2O7

Fig.1. Electrical resistivity of (Na1-xCax)2Ir2O7.

PS-08

Dynamical analyses of condensed-phase hydrogens using nuclear and elec-tron wave packet molecular dynamics simulation

K. Hyeon-Deuk1,2

1Department of Chemistry, Kyoto University, Kyoto, 606-8502, Japan 2Japan Science and Technology Agency, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan

Understanding microscopic dynamics of condensed-phase systems exhibiting strong quantum ef-fects is still one of the important open problems. Hydrogen is of primary importance not only in the fundamental condensed phase physics but also in its potential applications as energy source without harmful byproducts. Although hydrogen is the simplest of all molecular species, nuclear quantum ef-fects (NQEs) dominate properties of the condensed phases.

We recently proposed the real-time simulation method of nuclear and electron wave packet molec-ular dynamics (NEWPMD) based on the non-empirical intra- and inter-molecular interactions.[1,2,3] This is the first time that the real-time quantum molecular dynamics simulation without any model po-tentials for hydrogen interactions is developed and applied to condensed-phase hydrogens taking into account the NQEs such as nuclear delocalization and zero-point energy.

In the proposed method, the NQEs are non-perturbatively taken into account. Any electronic model potentials for hydrogen interactions including the intra- and inter-molecular energies of non-spherical hydrogen molecules do not need to be given in advance since all electrons are explicitly treated by fermionic EWPs to account for their correlations. Nevertheless, its computational cost is quite reasona-ble.

Liquid para-hydrogen (p-H2) typically exhibits the strong NQEs and thus anomalous static and dy-namical properties at low temperature. We confirmed that the NEWPMD successfully reproduces the experimental basic properties of p-H2 liquid such as radial distribution functions, self-diffusion coeffi-cients, and shear viscosities, demonstrating that the NEWPMD can be a powerful and efficient quan-tum MD simulation method to study nonequilibrium and dynamical processes of condensed-phase hy-drogens. Our recent project on dynamical analyses of solid p-H2 will be also mentioned in my presen-tation. These studies open a new area of hydrogen material research to understand anomalous quantum properties which are difficult to be accessible by use of conventional MD simulation techniques as well as usual density functional theories which generally lack a long-range dispersion force.

Dynamics snapshot of Liquid p-H2 at 25 K Dynamics snapshot of Solid p-H2 at 2.5 K

[1] K. Hyeon-Deuk and K. Ando, J. Chem. Phys. (Communication) 140 (2014) 171101. [2] K. Hyeon-Deuk and K. Ando, Phys. Rev. B 90 (2014) 165132. [3] K. Hyeon-Deuk and K. Ando, Chem. Phys. Lett. 532 (2012) 124.

PS-09

First Principle Calculation of Electronic Structures of Lanthanide Oxides with Pseudopotential Method

T. Hamada1 and T. Ohno2,3

1Central Research Laboratory, Hitachi Ltd., Hatoyama, Saitama, 250-0395, Japan 2National Institute for Materials Science, 1-1 Namiki,Tukuba, 305-0044, Japan

3Institute of Industrial Science, University of Tokyo, 4-5-1 Komaba, Tokyo 153-8505, Japan

First principle determination of electronic structures of strongly correlated electronic systems (SCESs) is a subject of substantial concern in solid state physics and electronic structure theory. The electronic structure of SCESs is known to be calculated by the density functional+U (DFT+U) method treating correlated electrons as real electrons and itinerant electrons as DFT electrons. Empirical U parameters are usually used for describing the on-site interaction between the correlated electrons, however, use of empirical U parameters tarnishes the statues of the method and lowers its calculation accuracy. In this study, we introduced the first principles DFT+U pseudopotential (DFT+U PP) method, which is free from any empirical parameters, and applied it to the electronic structure calculation of lanthanide oxides having correlated electrons. Our method is based on a fact that the DFT energy of a material is proportional to Un2, where n is the number of correlated electrons on the atom of the material. This method is an extension of the constraint DFT method introduced by McMahan et al.[1] for the linearized muffin-thin (LMTO) method. Our DFT+U calculations provided insulating electronic structures for lanthanide oxides, reproducing an experimental fact that they are insulating, in contrast to the conventional DFT PP calculation, which provided metallic electronic structures for them, as shown for Ce2O3 in Figure 1.

Fig. 1 Electronic density of states of Ce2O3 in the antiferromagnetic state: (a) GGA PP and (b) GGA+U PP calculation results.

References [1] A. K. McMahan et al. : Phys. Rev. B 38 (1988) 6650. [2] A. V. Prokoviev et al.: J. Alloys. Compd. 242 (1996) 41. [3] D. A. Andersson et al.; Phys. Rev. B. 75 (2007) 035109.

PS-10

Fano resonance between Higgs bound states and Nambu-Goldstone modes

T. Nakayama1, I. Danshita,2,3 T. Nikuni,4 and S. Tsuchiya5

1Institute for Solid State Physics, University of Tokyo, Kashiwanoha 5-1-5, Kashiwa 277-8581, Japan2Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku,

Kyoto 606-8502, Japan3Computational Condensed Matter Physics Laboratory, RIKEN, 2-1 Hirosawa, Wako, Saitama

351-0198, Japan4Department of Physics, Faculty of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku,

Tokyo 162-8601, Japan5Center for General Education, Tohoku Institute of Technology, 35-1 YagiyamaKasumi-cho,

Taihaku-ku, Sendai, Miyagi 162-8601, Japan

Stimulated by the recent report of observing the Higgs boson in elementary particle physics, thestudies of the Higgs modes have attracted a lot of attention in condensed matter physics. Up tothe present, many e!orts have been made to observe the Higgs modes in various condensed mat-ter systems, such as quantum dimer antiferromagnets [1], superconductors [2], charge-density-wave materials [3], superfluid 3He-B phase [4], and ultra-cold Bose gases in optical lattices [5,6].Thanks to an approximate particle-hole symmetry, these systems are nearly Lorentz-invariant[7] so that the Higgs mode emerges.We study collective modes of superfluid Bose gases in optical lattices combined with potentialbarriers. Bose gases in a su"ciently deep optical lattice are described by Bose-Hubbard (BH)model. We assume that the system is in the vicinity of the quantum phase transition to a Mottinsulator at a commensurate filling, and analyze the collective modes with the time-dependentGinzburg Landau (TDGL) equation [8] which is microscopically derived from BH model. In ahomogeneous system, an emergent particle-hole symmetry gives rise to two types of collectivemode: gapless Nambu-Goldstone (NG) mode and gapful Higgs mode [9]. Here, we considertwo kinds of potential barrier: one shifts the chemical potential that breaks the particle-holesymmetry, and the other changes the hopping amplitude that holds the particle-hole symmetry.In the presence of the latter barrier, we find bound states of the Higgs modes called Higgs boundstates that have binding energies lower than the bulk Higgs gap and are localized around thebarrier. We show that the former barrier couples the Higgs bound states with the NG modesuch that the NG mode incident to the barriers can exhibit Fano resonance mediated by thebound states.

References

[1]Ch. Ruegg, et al., Phys. Rev. Lett. 100, 205701 (2008).[2]R. Matsunaga, et al., Science 345 6201 (2014).[3]R. Yusupov, et al., Nat. Phys. 6, 681 (2010).[4]C. A. Collett, et al., J. Low Temp. Phys. 171, 214 (2013).[5]U. Bissbort, et al., Phys. Rev. Lett. 106, 205303 (2011).[6]M. Endres, et al., Nature 487, 454 (2012).[7]C. M. Varma, J. Low Temp. Phys. 126, 901 (2002).[8]M. P. A. Fisher, et al., Phys. Rev. B 40, 546 (1989).[9]E. Altman and A. Auerbach, Phys. Rev. Lett. 89, 250404 (2002).

PS-11

Convergence for the Groundstate Auxiliary Field method

Katsuaki Kobayashi1, Hans-Georg Matuttis1, Xiaoxing Wang2

1. Department of Mechanical Engineering and Intelligent Systems, Graduate School ofThe University of Electro-Communications, Chofugaoka 1-5-1, Chofu-shi, Tokyo 182-8585 Japan

2. Schlumberger K.K., Sagamihara-shi, 252-0206, Kanagawa Japan

For small Hubbard-clusters for which the numerical diagonalization results are known, weshow that for the groundstate auxiliary field method, the Monte-Carlo convergence of the energyis consistent with self-averaging quantities 1/

!LN (Number of sites L, number of Monte-Carlo

samples Ns), not only to 1/!N as for non-self-averaging quantities. We also discuss the final

error as obtained by the corresponding error in the Suzuki-Trotter decomposition and the e!ectthe sign has on the convergence.

PS-12

Theoretical Study of Charge-Spin-Orbital Fluctuations in Mixed ValenceSpinels: AlV2O4 and LiV2O4

A. Uehara1, H. Shinaoka,2 and Y. Motome1

1Department of Applied Physics, University of Tokyo, Hongo 7-3-1, Bunkyo-ku Tokyo 113-8656, Japan2Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland

We theoretically investigate the fluctuations in charge, spin, and orbital degrees of freedomin spinel oxides AB2O4. We are particularly interested in mixed valence compounds, in whichthe nominal number of d electrons at the B cation is not an integer. As the B cations comprisea pyrochlore lattice as shown in Fig. 1, the mixed valence spinels are a good playground for theinterplay of multiple degrees of freedom on the geometrically frustrated lattice structure. In thepresent study, we focus on two spinels, AlV2O4 and LiV2O4, which show puzzling, contrastingbehavior despite the common structure: AlV2O4 exhibits a peculiar structural phase transitionwith a self-organization of seven V clusters (heptamers) at 700 K [1], while LiV2O4 does notshow any transition down to the lowest temperature except for crossover to an unconventionalheavy fermion state at 20-30 K [2]. In order to clarify the origin of the contrasting behavior,we adopt the combined method between the first-principles calculation and the perturbation interms of electron correlations. Specifically, we construct the multiband Hubbard model by themaximally-localized Wannier function analysis for the LDA band structure. We then calculatethe generalized susceptibility, which includes all the information of fluctuations in charge, spin,and orbital sectors, by incorporating the electron correlations at the level of the random phaseapproximation.

For AlV2O4, we find that the dominant fluctuations appear in the vicinity of the ! point in theBrillouin zone. Although there are many eigenmodes entangled with each other, we unveil thatpeculiar charge fluctuations are sensitively enhanced by the inter-site Coulomb interaction. Theenhanced fluctuations are of !-bonding type with strong orbital dependence, as schematicallyshown in Fig. 2. The importance of similar !-bonding states in the hepmater formation wassuggested in the previous experimental and theoretical studies [1,3]. Hence, our results providea key for understanding of the self-organization in AlV2O4. In contrast, for LiV2O4, we find thatthe sixteen eigenmodes related to a1g orbital have relatively larger eigenvalues and well separatedfrom other modes even in the non-interacting case. We show that the on-site interaction enhancesthe optical-type spin fluctuations at an incommensurate wave number, as schematically shownin Fig. 3. In this fluctuation, the net spin fluctuation vanishes in the four-site tetrahedron. Thisfluctuation is enhanced at very low temperature, in the order of 10 K, which is suggestive of thepeculiar heavy fermion behavior in LiV2O4.

Fig. 1: Pyrochlorelattice.

Fig. 2: !-bonding fluctua-tion in AlV2O4.

1

2 3

4

1

2 3

4

Fig. 3: Optical-type spin fluctuationin LiV2O4.

References[1] Y. Horibe et al.: Phys. Rev. Lett. 96 (2006) 086406.[2] S. Kondo et al.: Phys. Rev. Lett. 78 (1997) 3729.[3] K. Matsuda et al.: J. Phys. Soc. Jpn. 75 (2006) 124716.

PS-13

Excitonic Multipole Order in a d-p Model with Parity Mixing Y. Sugita, S. Hayami, and Y. Motome

Department of Applied Physics, University of Tokyo, Hongo 7-3-1, Bunkyo-ku Tokyo 113-8656

Multipole orders have attracted much attention in condensed matter physics, as they lead to exotic electronic, transport, and optical properties. For instance, the multipole orders induced by the strong spin-orbit coupling and electron correlation have been extensively studied in various f-electron materi-als [1]. Recently, unconventional multipole orders associated with conventional electronic symmetry breaking have also been of great interests. A typical example is found in several pyrochlore com-pounds, such as Os and Ir pyrochlores [2-4]. In these compounds, a noncoplanar all-in/all-out type magnetic (dipole) order was discussed as a magnetic octupole order, which leads to unconventional phenomena [5]. Similar multipole orders (magnetic toroidal and quadrupole orders) were discussed theoretically on a zigzag chain [6,7] and a honeycomb lattice [8-11], paying attention to the effects of the atomic spin-orbit coupling and the mixing of different parity orbitals. In these previous works, however, multipole orders always appear subsidiary to the lower-rank electronic orders. It is important to explore the possibility of pure, primary multipole ordering for deeper understanding of the multipole physics. In particular, it will be interesting to explore yet another type of multipole orders for further exotic phenomena beyond those in f-electron systems.

In order to search such primary multipole orders, we consider a simple d-p model on a zigzag chain, which incorporates the spin-orbit coupling and the parity mixing. The model is considered as an ex-tension of the multi-orbital model discussed for excitonic orders [12]. Using the Hartree-Fock ap-proximation, we obtain the ground-state phase diagram of this model at half filling in a wide range of intra and interorbital Coulomb interactions. The result shows that a pure multipole ordered phase ap-pears as an intermediate phase between the band insulating phase with the d-p hybridization gap and the antiferromagnetic phase caused by the strong intraorbital Coulomb interaction. The intermediate phase has a magnetic quadrupole order with an excitonic nature from the orbital mixing, which is sta-bilized by the spin-orbit coupling and the parity mixing. We also find that the multipole ordered phase exhibits a peculiar band deformation with a shift of the band bottom in the momentum space in an ap-plied magnetic field. [1] Y. Kuramoto, H. Kusunose, and A. Kiss: J. Phys. Soc. Jpn. 78 (2009) 072001. [2] J. Yamaura et al.: Phys. Rev. Lett. 108 (2012) 247205. [3] K. Tomiyasu et al.: J. Phys. Soc. Jpn. 81 (2012) 034709. [4] H. Sagayama et al.: Phys. Rev. B 87 (2013) 100403(R). [5] T. Arima: J. Phys. Soc. Jpn. 82 (2013) 013705. [6] Y. Yanase: J. Phys. Soc. Jpn. 83 (2014) 014703. [7] S. Hayami, H. Kusunose, and Y. Motome: arXiv:1502.00057. [8] S. Hayami, H. Kusunose, and Y. Motome: Phys. Rev. B 90 (2014) 024432. [9] S. Hayami, H. Kusunose, and Y. Motome: Phys. Rev. B 90 (2014) 081115(R). [10] S. Hayami, H. Kusunose, and Y. Motome: arXiv:1409.2142. [11] S. Hayami, H. Kusunose, and Y. Motome: arXiv:1409.3657. [12] B. Zocher, C. Timm, and P. M. R. Brydon: Phys. Rev. B 84 (2011) 144425.

PS-14

Finite Temperature Phase Transition in Chiral Spin Liquids

J. Nasu1, M. Udagawa,2 and Y. Motome2

1Department of Physics, Tokyo Institute of Technology, Ookayama, 2-12-1, Meguro, Tokyo 152-85512Department of Applied Physics, University of Tokyo, Hongo 7-3-1, Bunkyo, Tokyo 113-8656

Quantum spin liquid (QSL) is an exotic quantum state of matter in insulating magnets, wherelong-range ordering is suppressed down to the lowest temperature (T ). Among many possiblerealizations of QSLs, the chiral spin liquid, in which the time reversal symmetry is broken,has attracted considerable interest in not only condensed matter physics but also quantuminformation. This is because its excitation is suggested to be a non-Abelian anyon that worksas an operator in topological quantum computing [1]. For exploring the possibility of quantumcomputing, it is important to clarify how thermal fluctuations act on the chiral spin liquids andtheir excitations.

In the present study, in order to reveal the thermodynamic properties in chiral spin liquids,we address the Kitaev model on the decorated honeycomb lattice depicted in Fig. 1. The groundstate properties of this model were originally predicted by A. Kitaev [1], and studied in detailby the exact solution by H. Yao and S. Kivelson [2]. The model exhibits two di!erent typesof the chiral spin liquids accompanied with non-Abelian and Abelian anyons in the groundstate. These two phases appear by changing the exchange parameters J and J ! for intra- andinter-triangles, respectively. Here, we investigate the finite-T properties in this extended Kitaevmodel by using the quantum Monte Carlo simulation in the Majorana representation that wedeveloped [3,4]. We find that the model exhibits the finite-T phase transition associated withtime reversal symmetry breaking. In the case of J ! ! J , we show that the phase transition is ofsecond order. This result is confirmed by a Monte Carlo simulation in the e!ective model in thelimit of J ! ! J : we show that the transition belongs to the two-dimensional Ising universalityclass. With decreasing J !/J , however, the phase transition is changed to first order, indicatingthe existence of the tricritical point in the phase diagram. Moreover, we calculate the Chernnumber and the thermal Hall conductivity. In the parameter region where the non-Abeliananyon excitation is expected, we find that these quantities become nonzero below Tc due to theedge current of itinerant Majorana fermions.

Figure 1: Schematic picture of a two-dimensional decorated honeycomb lattice. Inthe Kitaev model defined on this lattice, theinteractions on the dashed, dashed-and-dotted,and solid bonds are of Ising type with only thex, y, and z spin components, respectively. Inthe present calculations, we impose J = Jx =Jy = Jz (bold lines) and J ! = J !

x = J !y = J !

z

(thin lines).

References[1] A. Kitaev: Ann. Phys., 321 (2006) 2.[2] H. Yao and S. Kivelson: Phys. Rev. Lett. 99 (2009) 247203.[3] J. Nasu, M. Udagawa, and Y. Motome: Phys. Rev. Lett. 113 (2014) 197205.[4] J. Nasu, M. Udagawa, and Y. Motome: in preparation.

PS-15

Magnetization Process in a Frustrated Spin Ladder T. Sugimoto,1 M. Mori,2 T. Tohyama,1 and S. Maekawa2

1Department of Applied Physics, Tokyo University of Science, Niijuku 6-3-1, Katsushika, Tokyo 125-8585 2 Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 361-0198

Recently, a cascade of phase transitions induced by magnetic field has been observed in BiCu2PO6

[1,2], whose effective spin model, a frustrated two-leg spin ladder, bridges between the frustrated spin

chain and the non-frustrated spin ladder with one-half spins [2,3]. According to the theoretical studies,

the zigzag spin chain exhibits one-third plateau [4], although no plateau emerges in the non-frustrated

spin ladder [5]. Therefore, the simple question arises as to whether plateaux do appear in the frustrated

spin ladder, or not. To clarify the question, we calculate rung-coupling dependence and frustration de-

pendence of magnetization process by using density-matrix renormalization-group method. In this

calculation, we find some plateaux at m=1/2 and 2/3, which do not appear in both the frustrated spin

chain and the non-frustrated spin ladder, in addition to 1/3 plateau and some cusps [6]. We analytically

find out a correspondence between effective models in weak and strong rung-coupling limits, which

gives an explanation of the plateaux and cusps.

Our study is useful to analyze experimental data of BiCu2PO6. �

References [1] Y. Kohama, S. Wang, A. Uchida, K. Prsa, S. Zvyagin, Y. Skourski, R. D. McDonald, L. Balicas,

H. M. Ronnow, C. Rüegg, and M. Jaime, Phys. Rev. Lett. 109, 167204 (2012).

[2] A. A. Tsirlin, I. Rousochatzakis, D. Kasinathan, O. Janson, R. Nath, F. Weickert, C. Geibel, A. M.

Lauchli, and H. Rosner, Phys. Rev. B 82, 144426 (2010).

[3] T. Sugimoto, M. Mori, T. Tohyama, and S. Maekawa, Phys. Rev. B 87, 155143 (2013).

[4] K. Okunishi and T. Tonegawa, J. Phys. Soc. Jpn. 72, 479 (2003); Phys. Rev. B 68, 224422

(2003).

[5] D. Cabra, A. Honecker, P. Pujol, Phys. Rev. Lett., 79, 5126 (1997).

[6] T. Sugimoto, M. Mori, T. Tohyama, and S. Maekawa, arXiv:1409.4280.

PS-16

Topological quantum phase transition in an SU(N)-invariant spin chain

K. Tanimoto and K. Totsuka

1Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwake-Cho, Kyoto

606-8502, Japan

In traditional condensed-matter physics, high symmetry like SU(N) is realized in ratheridealized situations and has been used mainly as mathematical convenience. Recently, SU(N)-symmetric fermion systems were realized using alkaline-earth atoms loaded in optical lattices[1,2]. Since a variety of novel quantum phases are expected [3], theoretical understanding ofquantum phases in the SU(N) fermion systems is urgent. We focus on the Mott phase with Nfermions per site in one dimension where the e↵ective Hamiltonian is described by the SU(N)Heisenberg spin chain. Generally, gapped (bosonic) phases with SU(N)-symmetry are classifiedinto one trivial and N � 1 nontrivial topological classes [4]. With the entanglement spectrum[5], we found for N = 4 that the ground state of the above SU(N) Heisenberg model is in oneof these (symmetry-protected) topological phases [6].

In this presentation, we consider a variant of the SU(4) Heisenberg Hamiltonian with quadraticand cubic terms to investigate a quantum phase transition out of the topological phase. Usinginfinite Time-Evolving Block Decimation (iTEBD) method [7], we obtained the ground state,which is then characterized by the structure of low-lying entanglement spectrum. As a result,there is a topological-non-topological quantum phase transition between the SU(4) VBS andthe dimer phases. We also determined the transition point using the string and the dimer orderparameters.

References[1] A. V. Gorshkov, et al., Nature Phys. 6, 289 (2010).[2] S. Taie, R. Yamazaki, S. Sugawa, and Y. Takahashi, Nature Phys. 8, 825 (2012).[3] H. Nonne, et al., Europhys. Lett. 102, 37008 (2013);

V. Bois, et al., Phys. Rev. B 91, 075121 (2015).[4] K. Duivenvoorden and T. Quella, Phys. Rev. B 87, 125145 (2013).[5] H. Li, and F. Haldane, Phys. Rev. Lett 101, 010504 (2008).[6] K. Tanimoto and K. Totsuka, in preparation.[7] G. Vidal, Phys. Rev. Lett 98, 070201 (2007).

PS-17

Meron Crystals with Spin Scalar Chiral Stripes R. Ozawa,1 S. Hayami,1 M. Udagawa,1 Y. Motome,1

K. Barros,2 G. W. Chern,2 and C. D. Batista2 1Department of Applied Physics, University of Tokyo, Hongo 7-3-1, Bunkyo-ku Tokyo 113-8656

2Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545

Chiral magnets with noncoplanar spin structures, e.g., skyrmion crystals, have drawn a lot of at-tention for their peculiar transport phenomena and a wide variety of potential applications [1]. In these systems, the spin scalar chirality defined by the triple product of three spins plays an essential role because it acts as an effective magnetic field for electrons via the spin Berry phase mechanism. In fact, there have been several studies on spin-charge coupled systems, focusing on a ferroic spin scalar chiral ordering [2, 3, 4, 5]. Recently, a spatially-modulated spin scalar chiral ordering also draws considerable interest, as it might lead to a rich variety of novel electronic structures and transport phenomena [6]. However, the determination of precise magnetic structure requires consid-erable effort, since the chiral ordered state sometimes has quite a large magnetic unit cell, which is hard to treat numerically.

In this study, in order to explore such intriguing possibility of spatially�modulated chiral orders, we focus on multiple-Q orderings characterized by more than one wave vector, anticipated from the instability of Fermi surface [4, 7, 8]. Specifically, we consider the Kondo lattice model with the nearest- (t1) and third-neighbor (t3) hoppings on a square lattice. In this model, while tuning t1 and t3, the dispersion relation has four saddle points at the Lifshitz transition point. These saddle points give rise to the van Hove singularity in the density of states. Such singular behavior is expected to en-hance the instability of the Fermi surface. We calculate the low-temperature properties of the model by performing the efficient numerical simulation based on the Langevin dynamics for localized spins with the kernel polynomial method [9]. As a result, we show that spin scalar chiral stripes accompa-nied with double-Q ordering emerge around the Lifshitz transition point. Surprisingly, the obtained stripes are regarded as a crystal of peculiar spin textures called merons (half of the skyrmions) [10]. We also investigate the stabilizing mechanism by the analytical perturbation approach with respect to the spin-charge coupling as well as the numerical variational calculations for the ground state. We discuss transport properties induced by the novel spin scalar chiral stripes. References [1] N. Nagaosa, and Y. Tokura: Nat. Nanotech. 8 (2013) 899. [2] Y. Taguchi, Y. Oohara, H. Yoshizawa, N. Nagaosa, and Y.Tokura: Science 291 (2001) 2573. [3] K. Ohgushi, S. Murakami, and N. Nagaosa: Phys. Rev. B 62 (2000) R6065. [4] I. Martin and C. D. Batista: Phys. Rev. Lett. 101 (2008) 156402. [5] Y. Akagi and Y. Motome: J. Phys. Soc. Jpn. 79, (2010) 083711. [6] D. Solenov, D. Mozyrsky, and I. Martin: Phys. Rev. Lett. 108 (2012) 096403. [7] Y. Akagi, M. Udagawa, and Y. Motome: Phys. Rev. Lett. 108 (2012) 096401. [8] S. Hayami and Y. Motome: Phys. Rev. B 90 (2014) 060402(R). [9] K. Barros and Y. Kato: Phys. Rev. B 88 (2013) 235101. [10] C. L. Chien, F. Q. Zhu, and J. G. Zhu: Physics Today 60 (2007) 40.

PS-18

Chiral magnetic e!ect in insulators

Hiroyuki Fujita and Masaki Oshikawa

Institute for Solid State Physics, University of Tokyo, Kashiwanoha 5-1-5, Kashiwa 277-8581, Japan

Using the topological insulator multilayer[1] model originally proposed as a model of Weylsemimetal we discuss the possible realization of chiral magnetic e!ect in insulators. For pa-rameters giving an insulating phase, we calculated chiral magnetic conductivity of the modelusing the standard Kubo formula. Although the previous study[2] based on a formation of lan-dau levels implied that in the insulating phase chiral magnetic conductivity becomes zero, wefound that this is an artifact of the unbounded linear dispersion corresponding to the surfacestate dispersion of the topological insulator layers. Indeed, we could obtain a nonzero resultby introducing a cuto! " which is physically a bulk energy gap of these topological insulatorlayers. Moreover, we constructed the model which realizes nonzero chiral magnetic e!ect andhas completely periodic momentum space(BZ).

To uncover the role of the energy gap for chiral magnetic e!ect, we calculated finite frequencychiral magnetic conductivity of a massive Dirac model with a finite chiral chemical potential,which is known as the minimal insulating model realizing chiral magnetic e!ect. We foundthat the e!ect is rather enhanced for ! != 0 by the energy gap. This is because the presenceof the energy gap protects the system from low energy excitations which are the source ofthe characteristic discontinuity observed in the massless case[3] that reduces the low frequencyresponse to one third of ! = 0 one.

-p - p2p2 p

kzd

-4

-2

2

4Energy

Figure 1: Energy dispersion of the multilayer model with parameters realizing an insulatingphase.

1 2 3 4 5

w

m5-1

1

2

3

4

5

6

sch

s0

Figure 2: Frequency dependence of chiral magnetic e!ect of the massive Dirac model. Blue:Real part, Red: Imaginary part.

References[1]A. Burkov and L. Balents, Phys. Rev. Lett. 107 (2011).[2] A. A. Zyuzin, S. Wu, and A. A. Burkov, Phys. Rev. B 85, 165110 (2012).[3]D. E. Kharzeev and H. J. Warringa, Phys. Rev. D 80, 10(2009).

PS-19